Sensitivity of Bayes Procedures to the Prior Distribution

Abstract

In the statistical decision problem, let p⁰ be a given prior probability distribution and d₀ be the Bayes decision function under p⁰. Our basic approach is to find the nearest distribution to p⁰ for which the optimal decision function would lead to an expected saving of some fixed amount ϵ over using d₀. Hence, for any prior distribution nearer to p⁰ than this one, do is ϵ-Bayes. This sensitivity analysis is considered from two viewpoints, before and after performing the experiment. These results constitute a modification and extension of some recent results by Fishburn, Murphy, and Isaacs, and we make use of their basic approach and computing algorithm. Our modifications are applicable to their problem as well.